Analyze sequences with clean forward difference tables. Interpolate missing values and compare changing step behavior. Export clear reports and graphs for faster numeric decisions.
Enter comma-separated values. The calculator builds the forward difference table and optionally estimates a target value.
This sample uses y = x², so the second forward differences stay constant.
| x | y | Δy | Δ2y |
|---|---|---|---|
| 0 | 1 | 3 | 2 |
| 1 | 4 | 5 | 2 |
| 2 | 9 | 7 | 2 |
| 3 | 16 | 9 | — |
| 4 | 25 | — | — |
First forward difference
Δyi = yi+1 − yi
Higher-order forward difference
Δnyi = Δn−1yi+1 − Δn−1yi
Newton forward interpolation
y(x) = y0 + uΔy0 + [u(u−1)/2!]Δ2y0 + [u(u−1)(u−2)/3!]Δ3y0 + ... where u = (x − x0) / h
Forward differences describe how values change from one point to the next. Constant first differences suggest a linear pattern. Constant second differences often indicate a quadratic pattern. Newton forward interpolation is most appropriate when x values are evenly spaced.
It measures how y values change between successive x values, builds higher-order difference columns, and can estimate intermediate values when equal spacing supports Newton forward interpolation.
The difference table can still be formed without equal spacing, but Newton forward interpolation assumes a constant step size. Uneven spacing reduces the reliability of that interpolation formula.
A constant first difference usually indicates a linear relationship. In that case, the data changes by the same amount for every equal step in x.
A constant second difference commonly suggests a quadratic pattern. Many polynomial datasets reveal their degree through the order where differences become constant.
Yes. When x values are evenly spaced, it can estimate y at a target x using Newton forward interpolation. Outside the data range, that estimate becomes extrapolation.
Each new difference column uses adjacent values from the previous column. That removes one available position each time, so the triangular table narrows naturally.
The chart plots the original y values and the first forward differences. If an interpolated point is available, it also appears as a separate marker.
Export when you need documentation, classroom sharing, audit records, or a quick comparison in spreadsheets and reports. CSV is convenient for data work, while PDF suits presentation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.